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The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).
Correct answer is '1.25'. Can you explain this answer?
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The thickness of a sheet is reduced by rolling (without any change in ...
Draft = (ΔH)max=μ2R=0.052×300=0.75mm
Hence, final thickness of the sheet = 2 – 0.75 = 1.25mm
Hence, final thickness of the sheet = 2 – 0.75 = 1.25mm
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The thickness of a sheet is reduced by rolling (without any change in ...
Problem Statement:
The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).
Solution:
To find the minimum possible final thickness produced by the rolling process, we need to consider the reduction in thickness due to the rolling process.
1. Calculation of Reduction in Thickness:
The reduction in thickness can be determined using the formula:
$\frac{\Delta h}{h} = \left(\frac{d}{D}\right)^2 \times \ln\left(\frac{1}{\mu}\right)$
where:
- $\Delta h$ is the reduction in thickness
- $h$ is the initial thickness
- $d$ is the diameter of the rolls
- $D$ is the initial thickness of the rolls
- $\mu$ is the coefficient of friction at the roll-workpiece interface
Given:
- $h = 2\,mm$
- $d = 600\,mm$
- $\mu = 0.05$
Substituting the given values into the formula, we get:
$\frac{\Delta h}{2} = \left(\frac{600}{600}\right)^2 \times \ln\left(\frac{1}{0.05}\right)$
Simplifying the equation:
$\Delta h = 2 \times \ln\left(\frac{1}{0.05}\right)$
$\Delta h = 2 \times \ln(20)$
$\Delta h \approx 2 \times 3$
$\Delta h \approx 6\,mm$
2. Calculation of Minimum Possible Final Thickness:
The minimum possible final thickness can be determined by subtracting the reduction in thickness from the initial thickness. Therefore:
Minimum Possible Final Thickness = Initial Thickness - Reduction in Thickness
Minimum Possible Final Thickness = 2 - 6
Minimum Possible Final Thickness = -4
However, the minimum possible final thickness cannot be negative. Therefore, the minimum possible final thickness that can be produced by this process in a single pass is 0 mm.
Conclusion:
The minimum possible final thickness that can be produced by this rolling process in a single pass is 0 mm.
The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).
Solution:
To find the minimum possible final thickness produced by the rolling process, we need to consider the reduction in thickness due to the rolling process.
1. Calculation of Reduction in Thickness:
The reduction in thickness can be determined using the formula:
$\frac{\Delta h}{h} = \left(\frac{d}{D}\right)^2 \times \ln\left(\frac{1}{\mu}\right)$
where:
- $\Delta h$ is the reduction in thickness
- $h$ is the initial thickness
- $d$ is the diameter of the rolls
- $D$ is the initial thickness of the rolls
- $\mu$ is the coefficient of friction at the roll-workpiece interface
Given:
- $h = 2\,mm$
- $d = 600\,mm$
- $\mu = 0.05$
Substituting the given values into the formula, we get:
$\frac{\Delta h}{2} = \left(\frac{600}{600}\right)^2 \times \ln\left(\frac{1}{0.05}\right)$
Simplifying the equation:
$\Delta h = 2 \times \ln\left(\frac{1}{0.05}\right)$
$\Delta h = 2 \times \ln(20)$
$\Delta h \approx 2 \times 3$
$\Delta h \approx 6\,mm$
2. Calculation of Minimum Possible Final Thickness:
The minimum possible final thickness can be determined by subtracting the reduction in thickness from the initial thickness. Therefore:
Minimum Possible Final Thickness = Initial Thickness - Reduction in Thickness
Minimum Possible Final Thickness = 2 - 6
Minimum Possible Final Thickness = -4
However, the minimum possible final thickness cannot be negative. Therefore, the minimum possible final thickness that can be produced by this process in a single pass is 0 mm.
Conclusion:
The minimum possible final thickness that can be produced by this rolling process in a single pass is 0 mm.
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The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer?
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The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer?.
The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).Correct answer is '1.25'. Can you explain this answer?.
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